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%I #9 Jul 10 2024 13:43:16
%S 1,0,-4,36,129,3340,2287607,162104000,16943055268,4059346088384,
%T 474967482901952,221630954408019520
%N a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e a(5) = 3340:
%e [0, 5, 7, 3, 2]
%e [5, 0, 5, 7, 3]
%e [7, 5, 0, 5, 7]
%e [3, 7, 5, 0, 5]
%e [2, 3, 7, 5, 0]
%t a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
%Y Cf. A071079, A374341.
%Y Cf. A374386 (minimal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).
%Y Cf. A374068 (minimal permanent), A374390 (maximal permanent).
%K sign,hard,more
%O 0,3
%A _Stefano Spezia_, Jul 07 2024
%E a(11) from _Giorgos Kalogeropoulos_, Jul 10 2024
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